Robust and perfect tracking of discrete-time systems

We study in this paper the problem of robust and perfect tracking for discrete-time linear multivariable systems. By robust and perfect tracking, we mean the ability of a controller to track a given reference signal with arbitrarily small settling time in the face of external disturbances and initial conditions. A set of necessary and su$cient conditions under which the proposed problem is solvable is obtained and, under these conditions, constructive algorithms are given that yield the required solutions. As is general to discrete-time systems, the solvability conditions to the above problem are quite restrictive. To relax these conditions, we propose an almost perfect tracking scheme, which is capable of tracking references precisely after certain initial steps. 2001 Elsevier Science Ltd. All rights reserved.